Representations of the Automorphism Group of a Right-Angled Coxeter Group

Abstract

In 2009 Grunewald and Lubotzky published a paper in which they defined a family of linear representations of the automorphism group of a free group. In this dissertation, we will use their ideas to construct a family of linear representation of the automorphism group of a right-angled Coxeter group. We will then use graph-theoretic properties of the defining graph to systematically decompose the image group into a group of block upper triangular matrices.